Active probe for an atomic force microscope and method of use thereof

ABSTRACT

An AFM that combines an AFM Z position actuator and a self-actuated Z position cantilever (both operable in cyclical mode and contact mode), with appropriate nested feedback control circuitry to achieve high-speed imaging and accurate Z position measurements. A preferred embodiment of an AFM for analyzing a surface of a sample in either ambient air or fluid includes a self-actuated cantilever having a Z-positioning element integrated therewith and an oscillator that oscillates the self-actuated cantilever at a frequency generally equal to a resonant frequency of the self-actuated cantilever and at an oscillation amplitude generally equal to a setpoint value. The AFM includes a first feedback circuit nested within a second feedback circuit, wherein the first feedback circuit generates a cantilever control signal in response to vertical displacement of the self-actuated cantilever during a scanning operation, and the second feedback circuit is responsive to the cantilever control signal to generate a position control signal. A Z position actuator is also included within the second feedback circuit and is responsive to the position control signal to position the sample. In operation, preferably, the cantilever control signal alone is indicative of the topography of the sample surface. In a further embodiment, the first feedback circuit includes an active damping circuit for modifying the quality factor (“Q”) of the cantilever resonance to optimize the bandwidth of the cantilever response.

CROSS REFERENCE TO A RELATED APPLICATION

This application is a continuation-in-part of U.S. patent applicationSer. No. 09/280,160, filed Mar. 29, 1999, now U.S. Pat. No. 6,189,374.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to atomic force microscopes (AFMs) and,particularly, to an AFM and method of use thereof that combines an AFM Zposition actuator and a self-actuated cantilever to provide high qualityimages at greatly increased data collection rates.

2. Description of the Related Art

An Atomic Force Microscope (“AFM”), as described in U.S. Pat. No.RE34,489 to Hansma et al. (“Hansma”), is a type of scanning probemicroscope (“SPM”). AFMs are high-resolution surface measuringinstruments. Two general types of AFMs include contact mode (also knownas repulsive mode) AFMs, and cyclical mode AFMs (periodically referredto herein as TappingMode™ AFMs). (Note that TappingMode™ is a registeredtrademark of Veeco Instruments, Inc. of Plainview, N.Y.)

The contact mode AFM is described in detail in Hansma. Generally, thecontact mode AFM is characterized by a probe having a bendablecantilever and a tip. The AFM operates by placing the tip directly on asample surface and then scanning the surface laterally. When scanning,the cantilever bends in response to sample surface height variations,which are then monitored by an AFM deflection detection system to mapthe sample surface. The deflection detection system of such contact modeAFMs is typically an optical beam system, as described in Hansma.

Typically, the height of the fixed end of the cantilever relative to thesample surface is adjusted with feedback signals that operate tomaintain a predetermined amount of cantilever bending during lateralscanning. This predetermined amount of cantilever bending has a desiredvalue, called the setpoint. Typically, a reference signal for producingthe setpoint amount of cantilever bending is applied to one input of afeedback loop. By applying the feedback signals generated by thefeedback loop to an actuator within the system, and therefore adjustingthe relative height between the cantilever and the sample, cantileverdeflection can be kept constant at the setpoint value. By plotting theadjustment amount (as obtained by monitoring the feedback signalsapplied to maintain cantilever bending at the setpoint value) versuslateral position of the cantilever tip, a map of the sample surface canbe created.

The second general category of AFMs, i.e., cyclical mode or TappingMode™AFMs, utilize oscillation of a cantilever to, among other things, reducethe forces exerted on a sample during scanning. In contrast to contactmode AFMs, the probe tip in cyclical mode makes contact with the samplesurface or otherwise interacts with it only intermittently as the tip isscanned across the surface. Cyclical mode AFMs are described in U.S.Pat. Nos. 5,226,801, 5,412,980 and 5,415,027 to Elings et al.

In U.S. Pat. No. 5,412,980, a cyclical mode AFM is disclosed in which aprobe is oscillated at or near a resonant frequency of the cantilever.When imaging in cyclical mode, there is a desired tip oscillationamplitude associated with the particular cantilever used, similar to thedesired amount of cantilever deflection in contact mode. This desiredamplitude of cantilever oscillation is typically kept constant at adesired setpoint value. In operation, this is accomplished through theuse of a feedback loop having a setpoint input for receiving a signalcorresponding to the desired amplitude of oscillation. The feedbackcircuit servos the vertical position of either the cantilever mount orthe sample by applying a feedback control signal to a Z actuator so asto cause the probe to follow the topography of the sample surface.

Typically, the tip's oscillation amplitude is set to be greater than 20nm peak-to-peak to maintain the energy in the cantilever arm at a muchhigher value than the energy that the cantilever loses in each cycle bystriking or otherwise interacting with the sample surface. This providesthe added benefit of preventing the probe tip from sticking to thesample surface. Ultimately, to obtain sample height data, cyclical modeAFMs monitor the Z actuator feedback control signal that is produced tomaintain the established setpoint. A detected change in the oscillationamplitude of the tip and a resulting feedback control signal areindicative of a particular surface topography characteristic. Byplotting these changes versus the lateral position of the cantilever, amap of the surface of the sample can be generated.

Notably, AFMs have become accepted as a useful metrology tool inmanufacturing environments in the integrated circuit and data storageindustries. A limiting factor to the more extensive use of the AFM isthe limited throughput per machine due to the slow imaging rates of AFMsrelative to competing technologies. Although it is often desirable touse an AFM to measure surface topography of a sample, the speed of theAFM is typically far too slow for production applications. For instance,in most cases, AFM technology requires numerous machines to keep pacewith typical production rates. As a result, using AFM technology forsurface measurement typically yields a system that has a high cost permeasurement. A number of factors are responsible for these drawbacksassociated with AFM technology, and they are discussed generally below.

AFM imaging, in essence, typically is a mechanical measurement of thesurface topography of a sample such that the bandwidth limits of themeasurement are mechanical ones. An image is constructed from a rasterscan of the probe over the imaged area. In both contact and cyclicalmode, the tip of the probe is caused to scan across the sample surfaceat a velocity equal to the product of the scan size and the scanfrequency. As discussed previously, the height of the fixed end of thecantilever relative to the sample surface can be adjusted duringscanning at a rate typically much greater than the scanning rate inorder to maintain a constant force (contact mode) or oscillationamplitude (cyclical mode) relative to the sample surface.

Notably, the bandwidth requirement for a particular application of aselected cantilever is generally predetermined. Therefore, keeping inmind that the bandwidth of the height adjustment (hereinafter referredto as the Z axis or Z-position bandwidth) is dependent upon the tipvelocity as well as the sample topography, the required Z-positionbandwidth typically limits the maximum scan rate for a given sampletopography.

Further, the bandwidth of the AFM in these feedback systems is usuallylower than the open loop bandwidth of any one component of the system.In particular, as the 3 dB roll-off frequency of any component isapproached, the phase of the response is retarded significantly beforeany loss in amplitude response. The frequency at which the total phaselag of all the components in the system is large enough for the loop tobe unstable is the ultimate bandwidth limit of the loop. When designingan AFM, although the component of the loop which exhibits the lowestresponse bandwidth typically demands the focus of design improvements,reducing the phase lag in any part of the loop will typically increasethe bandwidth of the AFM as a whole.

With particular reference to the contact mode AFM, the bandwidth of thecantilever deflection detection apparatus is limited by a mechanicalresonance of the cantilever due to the tip's interaction with thesample. This bandwidth increases with the stiffness of the cantilever.Notably, this stiffness can be made high enough such that the mechanicalresonance of the cantilever is not a limiting factor on the bandwidth ofthe deflection detection apparatus, even though increased imaging forcesmay be compromised.

Nevertheless, in contact mode, the Z position actuator still limits theZ-position bandwidth. Notably, Z position actuators for AFMs aretypically piezo-tube or piezo-stack actuators which are selected fortheir large dynamic range and high sensitivity. Such devices generallyhave a mechanical resonance far below that of the AFM cantilever broughtin contact with the sample, typically around 1 kHz, thus limiting theZ-position bandwidth.

Manalis et al. (Manalis, Minne, and Quate, “Atomic force microscopy forhigh speed imaging using cantilevers with an integrated actuator andsensor,” Appl. Phys. Lett., 68 (6) 871-3 (1996)) demonstrated thatcontact mode imaging can be accelerated by incorporating the Z positionactuator into the cantilever beam. A piezoelectric film such as ZnO wasdeposited on the tip-side of the cantilever. The film causes thecantilever to act as a bimorph such that by applying a voltage dependentstress, the cantilever will bend. This bending of the cantilever,through an angle of one degree, or even less, results in microns of Zpositioning range. Further, implementing the Z position actuator in thecantilever increases the Z-position bandwidth of the contact mode AFM bymore than an order of magnitude.

Nevertheless, such an AFM exhibits new problems with the Z positioningwhich were not concerns with other known AFMs. For instance, the rangeof the Z actuator integrated with the cantilever is less than isrequired for imaging many AFM samples. In addition, because thepositioning sensitivity of each cantilever is different, the AFMrequires recalibration whenever the probe is changed due to a worn orbroken tip. Further, the sensitivity in some cases exhibits undesirablenon-linearity at low frequencies. These problems can make the Z actuatorintegrated with the cantilever a poor choice for general use as the Zactuator in commercial AFMs.

Furthermore, notwithstanding the above, in many AFM imagingapplications, the use of contact mode operation is unacceptable.Friction between the tip and the sample surface can damage imaged areasas well as degrade the tip's sharpness. Therefore, for many of theapplications contemplated by the present invention, the preferred modeof operation is cyclical mode, i.e., TappingMode™. However, thebandwidth limitations associated with cyclical mode detection aretypically far greater than those associated with contact mode operation.

In cyclical or non-continuous contact mode operation, the AFM cantileveris caused to act as a resonant beam in steady state oscillation. When aforce is applied to the cantilever, the force can be measured as achange in either the oscillation amplitude or frequency. One potentialproblem associated with cyclical mode operation is that the bandwidth ofthe response to this force is proportional to 1/Q (where Q is the“quality factor” of the natural resonance peak), while the forcesensitivity of the measurement is proportional to the Q of the naturalresonance peak. Because, in many imaging applications, the bandwidth isthe primary limiting factor of scan rate, the Q is designed to be low toallow for increased imaging speeds. However, reducing the Q of thecantilever correspondingly reduces force detection sensitivity, whichthereby introduces noise into the AFM image.

A further contributing factor to less than optimal scan rates incyclical mode operation is the fact that the amplitude error signal hasa maximum magnitude. Over certain topographical features, a scanning AFMtip will pass over a dropping edge. When this occurs, the oscillationamplitude of the cantilever will increase to the free-air amplitude,which is not limited by tapping on the surface. The error signal of thecontrol loop is then the difference between the free-air amplitude andthe setpoint amplitude. In this instance, the error signal is at amaximum and will not increase with a further increase in the distance ofthe tip from the sample surface. The topography map will be distortedcorrespondingly.

Finally, the maximum gain of the control loop in cyclical mode islimited by phase shifts, thus further limiting the loop bandwidth. Inview of these drawbacks, the Z position measurement for an atomic forcemicroscope is typically characterized as being slew rate limited by theproduct of the maximum error signal and the maximum gain.

As a result, AFM technology posed a challenging problem if the scan ratein cyclical mode was to be increased significantly. One general solutionproposed by Mertz et al. (Mertz, Marti, and Mlynek, “Regulation of amicrocantilever response by force feedback,” Appl. Phys. Lett. 62 (19)at 2344-6 (1993)) (hereinafter “Mertz”), but not directed to existingcyclical mode AFMs, included a method for decreasing the effective Q ofa cantilever while preserving the sensitivity of the natural resonance.In this method, a feedback loop is applied to the cantilever resonancedriver such that the amplitude of the driver to the cantilever ismodified based on the measured response of the cantilever. Thistechnique serves to modify the effective Q of the resonating cantileverand will be referred to hereinafter as “active damping.” Mertzaccomplished active damping by thermally exciting the cantilever byfirst coating the cantilever with a metal layer that had differentthermal expansion properties than the cantilever beam itself. Then, inresponse to the feedback signals, Mertz modulated a laser incident onthe cantilever, so as to apply a modified driving force.

Unfortunately, this scheme is not practical to implement in existingcyclical mode AFMs. In a typical AFM of this type, the cantileverextends from a substrate which is mounted mechanically to apiezo-crystal used to drive the cantilever at its resonance. Thecantilever is driven at its resonance either by vibrating the substratewith the piezo-crystal. In an alternative arrangement, the substrate isreplaced with a mechanical mounting structure which integrates thepiezo-crystal. In operation, the piezo-crystal is excited to drive thecantilever. When active damping is applied to such a structure,mechanical resonances other than that of the cantilever are excited, andthe gain of the active damping feedback cannot be increased enough tosignificantly modify the effective cantilever Q. Further, the Mertzdesign is prohibitively inflexible for systems contemplated by thepresent invention due to the fact that, among other things, themodulating laser only deflects the cantilever in one direction. Thisintroduces a frequency doubling effect that must be accounted for inprocessing the output. Overall, the Mertz system is complex and producesmarginally reliable measurements at undesirably slow speeds.

Moreover, when imaging biological samples in fluid, using a mechanicallycoupled piezo-crystal to drive the cantilever at its resonance requiresthe cantilever die to move distances commensurate with movement of thecantilever tip. As a result, the driving apparatus acoustically excitesthe entire fluid cell, thus disrupting imaging capabilities due to thelack of a clearly identifiable resonance in the cantilever response. Inaddition, the damping of the response caused by operating in fluid oftendramatically inhibits the data collection and imaging capabilities ofthe AFM. A system and method to enhance the response, and particularlyAFM sensitivity in such applications, is needed.

The field of AFM imaging was in need of a system which is operable inboth contact and cyclical mode and which realizes high quality images atfast imaging speeds. In particular, a system is desired that can modifythe effective Q of a resonating cantilever without exciting mechanicalresonances other than that of the cantilever. As a result, the systemshould optimize the Z-position bandwidth of the cantilever response tomaximize scanning/imaging speeds, yet preserve instrument sensitivity.Further, the system should be operable in both ambient air and in fluidto, for example, facilitate imaging surfaces of biological samples intheir natural environments. Ideally, the cantilever response will have aclearly identifiable resonance.

OBJECT AND SUMMARY

The present invention combines an AFM Z position actuator and aself-actuated Z position cantilever (both operable in cyclical mode andcontact mode), with appropriately nested feedback control circuitry toachieve high-speed imaging and accurate Z position measurements. Mostgenerally, the feedback signals applied to each of the actuators can beindependently monitored to indicate the topography of the samplesurface, depending upon the scan rate and sample topography.

In one embodiment of the present invention, the lower frequencytopography features of a sample, including the slope of the samplesurface, are followed by a standard Z actuator while the high frequencycomponents of the surface topography are followed by the self-actuatedcantilever. Preferably, two feedback loops are employed. The firstfeedback loop controls the self-actuated cantilever to maintain arelatively constant force between the tip of the cantilever and thesample surface. The second feedback loop controls the standard Zactuator, at a lower speed than the first feedback loop and serveseither (1) to keep the self-actuated cantilever within its operating Zrange or (2) to maintain the linearity of the positioning sensitivity ofthe cantilever when following low frequency topography. This embodimentalso allows for the standard Z actuator to be exclusively used foraccurate height measurements when the scan rate is sufficiently lowered,typically less than 500 μm/sec.

According to a preferred embodiment of the present invention, an AFMwhich operates in cyclical mode (i.e., TappingMode™) combines both theAFM Z actuator and the self-actuated cantilever with appropriatefeedback control in a system that oscillates the self-actuated actuatorwithout introducing mechanical resonances other than that of thecantilever. Most notably, the self-actuated cantilever is not oscillatedby vibrating a piezo-crystal mechanically coupled to the cantilever, butrather is oscillated at its resonance by directly exciting thepiezoelectric material disposed thereon. This eliminates mechanicalresonances in the coupling path which would otherwise be present.

As suggested above, the speed of a standard AFM in cyclical mode isgenerally limited by the loop bandwidth of the force detection circuitryand the Z positioning apparatus. A further limiting factor associatedwith standard AFMs pertains to phase shift contributions from thevarious components of the loop that accumulate to limit the gain of anotherwise stable operating system. Importantly, however, theself-actuated cantilever of the present invention does not havesignificant phase shift contributions at standard operating frequencies,even though the detection bandwidth of the AFM in cyclical mode is stilllimited by the width of the resonance peak of the cantilever. Therefore,the self-actuated cantilever feedback loop is considerably faster thanthe AFM Z position actuator feedback loop, when both are limited by thesame detection bandwidth. Notably, this embodiment also increases thespeed of the AFM Z actuator feedback loop by providing a larger errorsignal than that which is generated by the cyclical mode amplitudedeflection detector.

In addition, the combination of the standard AFM Z actuator and theself-actuated cantilever allows for greater flexibility in fast scanningcyclical mode. When the Z actuator feedback loop is disabled oroperating with low gain, the topography appears as the control signal tothe self-actuated cantilever. This control signal preferably also servesas the error signal for the AFM Z actuator feedback loop. When the gainof the second feedback loop is optimized, i.e., when the Z actuator isoperating as fast as possible without yielding unreliable output, thetopography then appears in the control signal for the AFM Z positionactuator. As a result, by incorporating the self-actuated cantileverwithin the control loop, the speed of obtaining highly accuratemeasurements can be increased. Also, as in the previous embodiment, thestandard Z actuator can be used to remove slope or non-linearities fromthe scan in the case in which the self-actuated cantilever follows thetopography of the sample surface. Further, as an alternative to astandard Z actuator such as a piezo-stack actuator, a thermal actuatordisposed on the self-actuated cantilever can be used.

Another preferred embodiment of the invention uses the integratedpiezoelectric element of a self-actuated cantilever to modify the Q ofthe mechanical resonance of the cantilever. In operation, as in theprevious embodiment, the cantilever resonance is excited with theintegrated piezoelectric element, rather than with a mechanicallycoupled driving piezo-crystal. The circuit which provides the cantileverdrive signal modifies the Q of the lever with feedback from the detecteddeflection signal.

In particular, according to one preferred embodiment, the deflectionsignal is phase shifted, preferably by 90 degrees, and added back to thecantilever drive signal. This feedback component of the drive signalmodifies the damping of the cantilever resonance (i.e., active damping)and thereby controllably decreases or enhances the Q. Alternatively, thedeflection signal can be fed to a differentiator to modify the Q of themechanical resonance of the cantilever. The differentiated signal isadded back to the cantilever drive signal as a feedback signal toprovide the active damping. Notably, in this alternative embodiment, theQ can be modified to provide active enhancement, for example, toincrease the sensitivity of the response. When modification of thecantilever Q is combined with the structure of the previously describedembodiment wherein the self-actuated cantilever is used for Zpositioning in synchronicity with an AFM Z position actuator, the scanspeed of the AFM in cyclical mode can be increased by an order ofmagnitude or more.

In yet another preferred embodiment, the AFM of the present invention isadapted for operation while at least partially submersed in fluid forimaging surfaces of, for example, biological substances. By using theintegrated high speed actuator of the present invention to excite theresonance of the cantilever, the system eliminates disruptive acousticexcitations produced by a typical biological AFM which uses a piezostack actuator. The integrated actuator can also perform the functionsof the conventional tip/sample actuator, thus enhancing the bandwidth ofthe mechanical system. As a result, the AFM of the present invention iscapable of imaging biological substances with increased imaging speedand integrity. In particular, the invention yields a clearlyidentifiable cantilever response (in both ambient air and fluid), thusallowing lower oscillatory drive voltages which, in turn, minimizes theforces between the tip and the sample. In addition, gasses (e.g.,corrosive gasses) can be introduced into the system without damaging theprobe. This capability permits the observance of real-time chemicalreactions between the gas and, typically, the biological sample.

These and other objects, features, and advantages of the invention willbecome apparent to those skilled in the art from the following detaileddescription and the accompanying drawings. It should be understood,however, that the detailed description and specific examples, whileindicating preferred embodiments of the present invention, are given byway of illustration and not of limitation. Many changes andmodifications may be made within the scope of the present inventionwithout departing from the spirit thereof, and the invention includesall such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

A preferred exemplary embodiment of the invention is illustrated in theaccompanying drawings in which like reference numerals represent likeparts throughout, and in which:

FIG. 1 is a schematic diagram illustrating an AFM according to thepresent invention including a self-actuated cantilever and feedbackcircuitry to control the cantilever in contact mode operation;

FIG. 2 is a schematic diagram illustrating an AFM according to a secondembodiment of the present invention including a self actuated cantileverand feedback circuitry to control the cantilever in cyclical modeoperation;

FIG. 3 is a schematic diagram illustrating a self-actuated AFMcantilever according to the present invention and a cantilever drivecircuit which modifies the quality factor (“Q”) of the cantilever;

FIG. 4 is a schematic diagram illustrating an AFM according to thepresent invention including a self actuated cantilever and feedbackcircuitry to control the cantilever in cyclical mode, and a cantileverdrive circuit for modifying the quality factor, i.e., Q, of thecantilever;

FIG. 5 is a schematic diagram illustrating a self-actuated AFMcantilever according to the present invention and an alternateembodiment of the cantilever drive circuit which modifies the qualityfactor (“Q”) of the cantilever;

FIG. 6 is a schematic diagram illustrating an AFM according to thepresent invention including a self actuated cantilever and feedbackcircuitry to control the cantilever in cyclical mode, and an alternateembodiment of the cantilever drive circuit for modifying the qualityfactor, i.e., Q, of the cantilever;

FIG. 7 is a perspective view of a probe assembly including aself-actuated cantilever having a thermal actuator integrated therewith;

FIG. 8 is a cross-sectional elevational view of an AFM according toanother embodiment of the present invention, adapted for fluidoperation;

FIG. 9 is a representation of another alternate embodiment of thepresent invention in which gasses are introduced to the sampleenvironment; and

FIG. 10 is a flow diagram illustrating AFM operation when making singlepixel measurements.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIEMENTS

Referring to FIG. 1, an AFM 10 according to the present invention, whichis configured for contact mode operation, is shown. AFM 10 includes twofeedback loops 12 and 14 that control an AFM Z position actuator 16 anda probe assembly 18, respectively. Probe assembly 18 includes aself-actuated cantilever 20 having a tip 26 that interacts with a sampleduring scanning. When scanning in contact mode, tip 26 generallycontinually contacts the sample, only occasionally separating from thesample, if at all. For example, at the end of a line scan tip 26 maydisengage the sample surface. While it scans the surface of the sample,cantilever 20 responds to the output of feedback loop 12 to ultimatelymap the topography of the surface of the sample, as described in furtherdetail below.

Cantilever 20 includes a fixed end 22 preferably mounted to an AFM mount(not shown) and a free distal end 24, generally opposite fixed end 22,that receives tip 26. In operation, the interaction between tip 26 andsample surface 28 causes the deflection of cantilever 20. To measurethis deflection, AFM 10 includes a deflection detector 30 that maypreferably be an optical detection system for measuring the cantileverdeflection by one of the following methods: (1) an optical beam bouncetechnique (see, e.g., Meyer and Amer, “Novel Optical Approach to AtomicForce Microscopy,” Appl. Phys. Lett. 53, 1045 (1988); Alexander,Hellemans, Marti, Schneir, Elings, Hansma, Longmire, and Gurley, “AnAtomic-Resolution Atomic-Force Microscope Implemented Using an OpticalLever,” Appl. Phys. Lett. 65 164 (1989)); (2) an interdigitaldiffraction grating technique (Manalis, Minne, Atalar, and Quate,“Interdigital Cantilevers for Atomic Force Microscopy,” Appl. Phys.Lett., 69 (25) 3944-6 (1996); Yoralioglu, Atalar, Manalis, and Quate,“Analysis and design of an interdigital cantilever as a displacementsensor,” 83(12) 7405 (June 1998)); or (3) by any other known opticaldetection method. These optical-based systems typically include a laserand a photodetector (neither shown) that interact according to one ofthe above techniques. When used in conjunction with very smallmicrofabricated cantilevers and piezoelectric positioners as lateral andvertical scanners, AFMs of the type contemplated by the presentinvention can have resolution down to the molecular level, and canoperate with controllable forces small enough to image biologicalsubstances.

Deflection detector 30 could also be a piezoresistor integrated into thecantilever with an associated bridge circuit for measuring theresistance of the piezoresistor (Tortonese, Barrett, and Quate, “AtomicResolution With an Atomic Force Microscope Using PiezoresistiveDetection,” Appl. Phys. Lett., 62, 8, 834-6 (1993)). Alternatively,deflection detector 30 could be a circuit for measuring the impedance ofthe piezoelectric element of self-actuated cantilever 20, or anothersimilarly related apparatus.

With further reference to FIG. 1, AFM 10 operates at a force determinedby a combination of a first signal having a setpoint value and acantilever detection signal generated by deflection detector 30. Inparticular, AFM 10 includes a difference amplifier 32 that receives andsubtracts the setpoint signal from the cantilever deflection signalthereby generating an error signal. Difference amplifier 32 transmitsthe error signal to a controller 34, preferably a PID(proportional-integral-derivative) controller, of feedback loop 12.Controller 34 can be implemented in either analog or digital, and mayapply either a linear gain or a gain characterized by a more complexcomputation. In particular, controller 34 can apply a gain to the errorsignal that is defined by one or more of a proportional, an integral ora differential gain.

Controller 34, in response to the error signal, then generates a controlsignal and transmits the control signal to a piezoelectric element 36disposed on self-actuated cantilever 20. By controlling the Z orvertical position of piezoelectric element 36 of cantilever 20 withfeedback control signals from controller 34, AFM 10 ideally operates tonull the error signal generated by difference amplifier 32. When theerror signal is nulled, the force between tip 26 and sample surface 28is maintained at a generally constant value equal to the setpoint. Notethat, optionally, a high voltage amplifier (not shown) may be employedto increase the voltage of the control signal transmitted to cantilever20, but is not required for most applications.

The control signal applied to cantilever 20 by controller 34 of feedbackcircuit 12 is also input, preferably as an error signal, to a secondfeedback circuit 14 such that first feedback circuit 12 is nested withinsecond feedback circuit 14. Feedback circuit 14 includes a secondcontroller 38 which, like controller 34, can be implemented in analog ordigital and may apply either a linear gain or a gain having a morecomplex computation. Controller 38 has a second input to which isapplied a comparison signal having a second setpoint value that is equalto the Z center point of the actuator that it controls, e.g., AFM Zposition actuator 16. Preferably, this setpoint is a zero coordinatevalue, thus making the cantilever control signal (the output ofcontroller 34) itself the error signal. Similar to controller 34,controller 38 (also preferably a PID controller) conditions the errorsignal (i.e., the difference of its input signals) with a gain that ischaracterized by one or more of a proportional, integral or differentialgain. Controller 38 generates a second feedback control signal that isultimately applied to Z position actuator 16 to effectively null the lowfrequency components of the control signal generated by feedback circuit12. A high voltage amplifier 40 may be employed to increase the voltageof the control signal output by controller 38 to Z position actuator 16and, for most position transducers of the scale contemplated by thepresent invention, such an amplifier 40 is required.

To operate at maximum scanning rate, the gain of the second feedbackloop 14 which controls Z position actuator 16, is reduced to zero orsome small value. As a result, at a scanning rate greater than about 500μm/sec, the topography of sample surface 28 appears as the feedbackcontrol signal applied to self-actuating cantilever 20 by first feedbackloop 12. In this case, Z position actuator 16 may be controlled in apre-programmed manner to follow the slope of sample surface 28 or toeliminate coupling due to the lateral scanning of tip 26.

Further, in this embodiment, the sensitivity of the self-actuatedcantilever 20 can be calibrated with the standard Z position actuator16. Sensitivity calibration is accomplished by moving the two actuators16 and 36 in opposite directions to achieve a zero net movement of thetip 26 as measured by force deflection detector 30, and comparing therespective non-zero control signals required to accomplish this zero netmovement.

Turning to FIG. 2, an AFM 50 according to another preferred embodimentof the invention, designed for TappingMode™ or cyclical mode operation,is shown. AFM 50, like the embodiment show in FIG. 1, includes twofeedback circuits (loops) 52 and 54 that respectively controlself-actuated cantilever 20 of probe assembly 18 and AFM Z positionactuator 16. AFM 50 also includes an oscillator 56 that vibratesself-actuated cantilever 20 by applying an oscillating voltage directlyto piezoelectric element 36 of self-actuated cantilever 20. Theresulting oscillation of the cantilever 20 can be characterized by itsparticular amplitude, frequency and phase parameters. Note that AFM Zposition actuator 16 is preferably a piezo-tube actuator, and a sampleto be analyzed is disposed on the piezo-tube actuator such that movementof actuator 16 is generally normal to the scanning surface 28 of thesample.

When tip 26 is in close proximity to sample surface 28, the forceinteraction between tip 26 and sample surface 28 modifies the amplitudeof vibration in cantilever 20. Similar to the contact mode embodimentshown in FIG. 1, deflection detector 30 measures the deflection ofcantilever 20 by an optical beam bounce technique, an interdigitaldiffraction grating technique, or by some other optical detection methodknown in the art.

In operation, once detector 30 acquires data pertaining to cantileverdeflection, detector 30 generates a deflection signal which isthereafter converted to an RMS amplitude signal by an RMS-to-DCconverter 58 for further processing by loop 52. Note that,alternatively, lock-in detection, or some other amplitude, phase, orfrequency detection technique may be used as an alternative to RMS-to-DCconverter 58.

The operating RMS amplitude of the cantilever vibration is determined atleast in part by the setpoint value. A difference amplifier 32 subtractsa signal corresponding to the setpoint value from the cantileverdeflection signal output by converter 58. The error signal generated bydifference amplifier 32 as a result of this operation is input tocontroller 34. Controller 34 (again, preferably a PID controller)applies one or more of proportional, integral and differential gain tothe error signal and outputs a corresponding control signal. Controller34 then applies this control signal to piezoelectric element 36 ofself-actuated cantilever 20 to control the Z position of cantilever 20as the cantilever traverses varying topography features of the samplesurface. By applying the feedback control signal as described, feedbackloop 52 ultimately nulls the error signal such that, e.g., theoscillation amplitude of cantilever 20 is maintained at the setpointvalue.

A summing amplifier 60 then sums the feedback control signal output bycontroller 34 with the output of driving oscillator 56 so as to applythe feedback cantilever control signal to element 36. Note that a highvoltage amplifier (not shown) may be employed to increase the voltage ofthe summed signal output by amplifier 60 and applied to piezoelectricelement 36 of cantilever 20, but is not required.

The control signal applied to summing amplifier 60 from the controller34 is also input to controller 38 as the error signal of second feedbackloop 54 such that first feedback loop 52 (similar to feedback loop 12 ofthe contact mode embodiment of FIG. 1) is nested within second feedbackloop 54. Controller 38 has a second input that receives a comparisonsignal having a second setpoint value that is equal to the Z centerpoint of the actuator that it controls, e.g., the AFM Z actuator 16.Preferably, this setpoint value is a zero coordinate value such that thecantilever control signal is itself the error signal. Controller 38applies one or more of proportional, integral and differential gain tothe error signal and outputs a corresponding control signal forcontrolling Z position actuator 16, and therefore the Z position of thesample. This control of the Z position of the sample operates toeffectively null the low frequency components of the self-actuatedcantilever control signal generated by feedback circuit 52. Note that ahigh voltage amplifier 40 may be employed between the output ofcontroller 38 and the input of Z position actuator 16 to increase thevoltage of the control signal applied by controller 38 to Z positionactuator 16, and is required for most position transducers of the scalecontemplated by the present invention.

During fast scanning operation, as in the previously describedembodiment, the gain of second feedback loop 54, which controls Zposition actuator 16, is preferably reduced to zero or some small value.In this cyclical mode case, Z position actuator 16 may be controlled,e.g., in a pre-programmed manner, to either follow the slope of samplesurface 28 or to eliminate coupling due to the lateral scanning of tip26. When the gain of second feedback loop 54 is optimized, the controlsignal output by loop 54 is indicative of the sample topography. As aresult, depending upon scanning rate, the feedback cantilever controlsignals output by loop 52, and corresponding to particular lateralcoordinates, are indicative of the topography of sample surface 28.These signals can then be further processed to create an image of thesample surface.

The bandwidth of the amplitude detection of the cantilever in cyclicalmode or in non-contact mode is limited by the frequency width of themechanical resonance peak of the cantilever, which is defined by the 3dB roll-off frequencies. In particular, the 3 dB roll-off is equal tof/2Q, where f is the center frequency of the resonance peak and Q is thequality factor of the cantilever resonance peak. As such, the width ofthe resonance peak is proportional to the quality factor Q of theresonance peak.

FIG. 3 shows schematically how the Q (quality factor of the cantileverresonance peak) of self-actuated cantilever 20 can be modified using adeflection feedback technique. Generally, an active damping feedback orcantilever drive circuit 62 modifies the oscillating voltage output by adriving oscillator 66 (and applied directly to piezoelectric element 36of cantilever 20) to optimize the bandwidth of amplitude detection.Active damping circuit 62 utilizes a deflection detector 30 that, asdescribed with respect to FIGS. 1 and 2, is preferably an opticaldetection system including a laser and a photodetector, and whichmeasures cantilever deflection by an optical beam bounce technique oranother conventional technique. Alternatively, as in the previouslydescribed embodiments, deflection detector 30 could be (1) apiezoresistor integrated into cantilever 20 with an associated bridgecircuit for measuring the resistance of the piezoresistor, or (2) acircuit for measuring the impedance of the piezoelectric element 36 ofself-actuated cantilever 20.

As it senses a deflection of cantilever 18, deflection detector 30transmits a corresponding deflection signal to a damping element ofactive damping circuit 62. In one preferred embodiment, the dampingelement is a phase shifter 64 that advances or retards the phase of thesensed deflection signal by 90 degrees. This phase shift acts as adamping component of the oscillatory motion of cantilever 20 to modifythe Q of the mechanical resonance of the cantilever. The phase-shifteddeflection signal is then summed with the output of a driving oscillator66 by a summing amplifier 68.

The relative gain of the oscillator signal amplitude to the phaseshifted deflection signal determines the degree to which the Q of thecantilever resonance is modified, and therefore is indicative of theavailable bandwidth. Note that the ratio of the two summed signals canbe scaled at summing amplifier 68 to determine the extent to which thecantilever resonance is modified. Alternatively, a gain stage 65 couldbe inserted between phase shifter 64 and summing amplifier 68 to scalethe phase-shifted signal and obtain the resonance modifying data.

In sum, by actively damping the oscillation voltage to modify the Q asdescribed above, damping circuit 62 ideally optimizes the bandwidth ofthe response of the cantilever 20. As a result, the AFM can maximizescan rate, yet still maintain an acceptable degree of force detectionsensitivity.

FIG. 4 shows an AFM 80 according to an alternate embodiment of thepresent invention incorporating the features of AFM 50 (cyclical modeconfiguration—FIG. 2), including two nested feedback loops 82 and 54,with the features of active damping circuit 62 (FIG. 3) to modify the Qof cantilever 20 in fast scanning cyclical mode operation. By activelydamping the resonance of cantilever 20 with feedback signals output bycircuit 62, the force detection bandwidth rises proportionally with acorresponding decrease in the Q. By combining a decrease in Q with thecontrol features of AFM 50 (FIG. 2), AFM 80 realizes much greater loopbandwidth in cyclical mode, thus achieving much greater (and much morecommercially viable) throughput per machine.

With specific reference to FIG. 4, AFM 80 operates as follows.Initially, the deflection signal obtained by deflection detector 30during a scanning operation is phase shifted by phase shifter 64 ofactive damping circuit 62. As noted above, the phase of the deflectionsignal is advanced or retarded by 90 degrees such that it acts as adamping component of the oscillatory motion of cantilever 20, thusmodifying the cantilever Q. The phase-shifted deflection signal is thensummed with the output of oscillator 66 by summing amplifier 68.

The ratio of the two summed signals can be scaled at summing amplifier68 to determine the extent to which the cantilever resonance ismodified. Alternatively, as described in connection with FIG. 3, a gainstage 65 can be inserted between the phase shifter and the summingamplifier to scale the phase-shifted signal. The output of summingamplifier 68 is then further amplified (with amplifier 70) to a suitablevoltage for driving piezoelectric element 36 of self-actuated cantilever20.

With further reference to FIG. 4 and the more specific operation of AFM80, the output of amplifier 70 drives self-actuated cantilever 20 at afrequency equal to that of the natural resonance of cantilever 20,wherein the Q of the driving frequency is modified by active dampingcircuit 62 to increase overall loop bandwidth. Moreover, this change inQ increases the speed of data collection, for example, viascanning/imaging. Because the piezoelectric element 36 disposed oncantilever 20 is used to drive cantilever 20 at its resonant frequency,the oscillating voltage in this embodiment can be applied directly tocantilever 20 without introducing extraneous mechanical resonances intothe system.

When the tip 26 is in close proximity to sample surface 28, the forceinteraction between tip 26 and sample surface 28 modifies the amplitudeof vibration in cantilever 20. The deflection signal generated by thedeflection detector 30 in response to a detected change in the amplitudeof vibration is then converted to an RMS amplitude signal by RMS to DCconverter 58 to facilitate further processing. Notably, lock-indetection or some other amplitude, phase, or frequency detectiontechnique may be used in place of RMS to DC converter 58.

Similar to AFM 50, the operating RMS amplitude of the cantilevervibration is determined (at least in part) by the setpoint value, whichis subtracted from the cantilever deflection signal by differenceamplifier 32. The error signal generated by difference amplifier 32 isinput to controller 34. Controller 34 applies one or more ofproportional, integral and differential gain to the error signal andcontrols piezoelectric element 36 of self-actuated cantilever 20 to nullthe error signal, thus ensuring that the amplitude of cantileveroscillation is kept generally constant at a value equal to the setpoint.A high voltage amplifier (not shown) may be employed to increase thevoltage of the signal to cantilever 20, but is not required.

The control signal transmitted by controller 34 to cantilever 20 is alsoinput to controller 38 of second feedback loop 54 such that firstfeedback loop 82 is nested within second feedback loop 54. Preferably,the second setpoint input to controller 38 is a zero value associatedwith AFM actuator 16, in which case the cantilever control signal isitself the error signal conditioned by controller 38. Again, PIDcontroller 38 applies one or more of proportional, integral anddifferential gain to the error signal for ultimately controlling Zposition actuator 16 to null the low frequency components of the controlsignal applied to the self-actuated cantilever, when scanning at anoptimum rate. Further, as highlighted above, a high voltage amplifier 40may be employed to increase the voltage of the control signal applied toZ position actuator 16, and is required for most position transducers ofthe scale contemplated by the present invention.

In sum, AFM 80 combines an AFM Z actuator 16 with a self-actuatedcantilever 20 in a manner that allows both high speed imaging andaccurate Z position measurement by decreasing the effective Q ofcantilever 20 with damping circuit 62. Damping circuit 62 activelymodifies the oscillating voltage signal output by oscillator 66, whilepreserving the sensitivity of the natural resonance, to insure that thebandwidth of the cantilever response is optimized. Further, dependingupon the particular sample topography and the scan rate, the topographycan be mapped by monitoring one of the feedback control signalsindependent of the other.

In an alternative embodiment to the deflection feedback circuitry shownin FIG. 3, a cantilever drive circuit 109 includes a damping elementthat comprises a differentiator 110, as shown in FIG. 5. Differentiator110 , in conjunction with an adjustable gain stage 116, provides asignal that is a very close approximation to the damping component ofthe cantilever oscillation so as to change the system Q. Moreparticularly, differentiator 110 differentiates the deflection signalsensed by deflection detector 30 during operation. The differentiatedsignal is then applied to the gain stage 116. The gain applied by gainstage 116 is adjusted to selectively modify the Q of the cantilever soas to realize a desired Q, Q_(new).

Next, the differentiated deflection signal is applied to summingamplifier 68 and summed with the output of driving oscillator 66 toprovide the modified oscillating voltage, similar to active dampingcircuit 62 described previously. Prior to applying the modifiedoscillating voltage to cantilever 20, an amplifier 70 amplifies theoutput of summing amplifier 68 to a suitable voltage for drivingpiezoelectric element 36 of self-actuated cantilever 20. Duringoperation, the output of amplifier 70 drives self-actuated cantilever 20at the mechanical resonance of cantilever 18. In addition, althoughdifferentiator 110 can be implemented digitally, preferably it is ananalog differentiation circuit.

Notably, differentiator 110 (with appropriate gain provided by gainstage 114) can be used not only for active damping, but for activeenhancement (i.e., to increase the Q) as well. For example, whenoperating in fluid, the viscous forces present in the system cansignificantly damp the system response. Therefore, to counter thedamping effects of these forces, differential gain can be used toincrease the Q. Although such operation can decrease operation speed,the sensitivity of the response is enhanced, thus facilitating reliabledata collection. Moreover Q enhancement allows the AFM to output alarger data signal that is easier to process. Among other applications,active enhancement is particularly useful when imaging soft samples inair because the increased force sensitivity allows greater control ofthe drive voltage (e.g., greater control over the tip-sampleinteraction), thus minimizing the chance of damaging the sample.

Cantilever drive circuit 109 includes two additional branches, oneincluding an integrator 112 having an output coupled to a correspondingamplifier 118 to provide integral gain, while the other comprises anamplifier 114 that provides proportional gain. Integrator 112 and theassociated amplifier 118 process the cantilever deflection signal so asto tune the feedback response in conventional fashion. The proportionalgain provided by amplifier 114, on the other hand, can be used toactively modify the response of the cantilever. In particular, amplifier114 applies proportional gain, preferably to change the resonantfrequency of the cantilever, which, as discussed previously, is thepreferred frequency of operation. Cantilever drive circuit 109 willemploy proportional gain if, for example, the system experiencessignificant noise at the operational resonant frequency. Such noise cansignificantly compromise data collection and imaging capabilities suchthat, by shifting the resonant frequency with proportional gain,cantilever drive circuit 109 permits the AFM to operate at a frequencywhere noise is not a significant limitation.

Amplifiers 114, 116 and 118 are preferably independently adjustable withpositive and negative polarities. Amplifiers 114, 116, 118 arecontrolled either manually, typically as the user observes the AFMoutput, or automatically via, for example, a central processing unit 120or microprocessor, which computes the proper gain in response to thedesired Q, preferably input by the operator. CPU 120 can use analgorithm embedded in memory to intelligently apply differential,proportional and integral gain in response to analyzing the deflectionsignal, thus optimizing AFM operation in terms of speed and datacollection quality, as described previously.

To determine the proper amount of gain to be applied for a desiredresponse, the AFM is modeled. According to the preferred embodiment, thefeedback system shown in FIG. 5 can be characterized by the followingequation, $\begin{matrix}{\frac{V_{o}}{V(\omega)} = \frac{\gamma \quad k\quad {{\eta\chi}(\omega)}}{1 - {\gamma \quad k\quad {{\eta\chi}(\omega)}\quad {G(\omega)}}}} & \text{Eqn.~~1}\end{matrix}$

wherein χ_((ω)) is the cantilever response, γk is the response of thepiezoelectric element, (zinc oxide for example), η is the response ofthe deflection detector 30 (e.g., a photodiode sensor) and G(ω) is thegain to be applied. The response of the piezoelectric element (γk) andthe response of the photodiode (η) are predetermined according to thetype of cantilever used and therefore define constants in Equation 1.

The cantilever can be modeled as a basic second-order system having afrequency-based response characterized by the following equation,$\begin{matrix}{{\chi (\omega)} = \frac{\omega_{o}^{2}/k}{\omega_{o}^{2} - \omega^{2} + \frac{\quad {\omega\omega}_{o}}{Q}}} & \text{Eqn.~~2}\end{matrix}$

wherein ω_(o) is the resonant frequency of the cantilever, ω is theoperational frequency of the system, k is the spring constant, and Q isthe native Q of the system (a quantity that is measured duringoperation). Therefore, the system response becomes, $\begin{matrix}{\frac{V_{o}}{V(\omega)} = \frac{\gamma \quad {\eta\omega}_{o}^{2}}{\left( {\omega_{o}^{2} - \omega^{2}} \right) + \frac{\quad {\omega\omega}_{o}}{Q} - {\gamma \quad {\eta\omega}_{o}^{2}{G(\omega)}}}} & \text{Eqn.~~3}\end{matrix}$

where G(ω) can be any physically realizable function, real or imaginary,so as to provide proportional, differential, integral, ω², etc. gain.

More particularly, the expression$\frac{\quad {\omega\omega}_{o}}{Q}$

is the term representative of differentiator 110 and, therefore, is theterm that is manipulated to modify cantilever damping. To modifycantilever damping, i.e., to modify the Q of the cantilever, the gain isset according to the following equation, $\begin{matrix}{{G(\omega)} = {\quad \frac{\omega}{\omega_{o}}\frac{1}{\gamma \quad \eta}\left( {\frac{1}{Q} - \frac{1}{Q_{new}}} \right)}} & \text{Eqn.~~4}\end{matrix}$

where, again, Q is the native Q, and Q_(new) is the desired Q foroptimum operation.

When substituting the gain (Eqn. 4) into the system response as definedby Eqn. 3, the response remains the same except that the native Q isreplaced by the desired Q, Q_(new). In particular, the system responsebecomes, $\begin{matrix}{\frac{V_{o}}{V(\omega)} = \frac{\gamma \quad {\eta\omega}_{o}^{2}}{\left( {\omega_{o}^{2} - \omega^{2}} \right) + \frac{\quad {\omega\omega}_{o}}{Q_{new}}}} & \text{Eqn.~~5}\end{matrix}$

As an example, in computing the gain as defined in Eqn. 4, we can assumethat the phase is 90° and that ω equals ω_(o) (which is preferably thecase where the AFM is operated at the resonant frequency of thecantilever). As a result, the gain becomes, $\begin{matrix}{{{Abs}(G)} = {\frac{1}{\gamma \quad \eta \quad Q} - {\frac{1}{\gamma \quad \eta} \cdot \frac{1}{Q_{new}}}}} & \text{Eqn.~~6}\end{matrix}$

For a Q=300 Å/V, γ=200 Å/V and η=0.33 mV/Å, the gain is equal to0.05−14.9/Q_(new). Q_(new) can be input manually by the user, or it canbe intelligently selected according to an algorithm embedded in CPU 120.

For example, an algorithm for selecting a Q using computer 120 takesinto consideration the spatial frequency of the sample topography, thescan size, and the scan rate which are input by the operator. Theproduct of the scan size and the scan rate is the tip velocity. In onepreferred embodiment, the algorithm is an open loop algorithm that makesan assumption about the sample topography and then scales the desired Q,Q_(new), for the selected tip velocity. Notably, because any AFM imageis ultimately a convolution of the sample topography and the probe tip,a limit to the spatial frequency of the topography is considered to bethe geometry of the probe tip. Alternatively, a closed loop algorithmincludes a subroutine of a gain setting algorithm for the Z feedbackloop. One such known algorithm selects the optimum integral andproportional gain of the Z feedback loop by maximizing theautocorrelation function of the trace and retrace scan lines.Preferably, once this routine is executed, a damping subroutine uses thefeedback loop error signal (RMS-setpoint) to determine if enough gain isbeing used (i.e., the routine determines whether the error signal isbelow a predetermined threshold). To achieve more gain, the Q isdecreased, and then the gain setting routine is reinitiated. If the Qreaches a predetermined minimum value, then the gain setting routineoperates to reduce the scan rate for optimum operation.

In general, computer 120 outputs a control signal that is communicatedto one of the gain stages 114, 116, 118 for applying the appropriategain to optimize AFM operation. To modify the Q of the cantilever, theresponse of both the piezoelectric element 20 and the deflectiondetector 30 are set according to the type of cantilever used. Based onthe desired Q (i.e., Q_(new)) computer 120 generates a control signaland transmits the control signal to, for example, gain stage 114 so asto cause gain stage 114 to apply the appropriate gain to the detecteddeflection signal to increase AFM operating speed, thus reducing Q_(new)and increasing the damping or drag. Alternatively, gain can be computedso as to enhance the Q and therefore decreasing the damping. In thisalternative, the AFM is slowed correspondingly; however, thesignal-to-noise ratio, as well as the force sensitivity, increases, thusproviding advantages in terms of increased control over tip-sampleinteraction and operational convenience.

Overall, Q modification using phase shifting (FIGS. 3 and 4) is similarto using differential gain (FIGS. 5 and 6) to modify the Q. However,phase shifting behaves like differential gain only in a narrow bandwidthwhen the phase shifter is adjusted correctly (i.e., 90°). When the phaseshifter is out of adjustment, phase shifting behaves like a linearcombination of differential and proportional gains, thus shifting theresonant frequency as well as modifying the quality factor, Q of thecantilever. Because AFM cantilevers typically have some variation intheir natural resonant frequencies, the phase shifter 64 (FIGS. 3 & 4)must be adjusted whenever the cantilever is changed, which can be quiteoften. With separate differential and proportional gain, cantileverdrive circuit 109 modifies the damping and the resonant frequencyindependently without significant sensitivity to different naturalresonant frequencies of different cantilevers.

Similar to FIG. 4, FIG. 6 shows an AFM 130 according to an alternateembodiment of the present invention incorporating the features of AFM 50(cyclical mode configuration—FIG. 2), including two nested feedbackloops 132 and 54. AFM 130 also includes the features of cantilever drivecircuit 109 (FIG. 6) to modify the Q of cantilever 20 in fast scanningcyclical mode operation. Alternatively, by combining the controlfeatures of AFM 50 (FIG. 2) with active enhancement provided bycantilever drive circuit 109, AFM 130 can, for example, increase theforce sensitivity to facilitate imaging soft samples even thoughthroughput may decrease. As described previously in conjunction withFIG. 5, enhancing the Q is particularly useful when operating in fluid,e.g., when imaging biological samples, because the viscous environmentcan have a detrimental damping effect on the Q. Overall, AFM 130 ispreferably operated as fast as possible without significantlycompromising force sensitivity.

Referring specifically to FIG. 6, AFM 130 is similar to AFM 80 exceptthat cantilever drive circuit 109 is substituted for damping circuit 62.As a result, AFM 130 has the same capabilities of AFM 80. However, inaddition, AFM 130 provides proportional and integral gain, as well asactive Q enhancement which is implemented with applied differentialgain, as described above in conjunction with FIG. 5.

When changing the Q of the cantilever, the resonant or peak amplitude ofcantilever response also changes. Generally, the ratio between theamplitude and the Q will remain constant such that if you decrease the Qby a factor of two, the amplitude will correspondingly decrease by afactor of two. Notably, it is often times desired to hold the amplitudeconstant while changing the cantilever Q to avoid having to constantlyre-scale the drive to either observe the change in Q, or use theactively modified response. Re-scaling the drive can be time consumingand often times is difficult. However, implementing a system that holdspeak amplitude constant while changing the Q is not obvious. This is dueto the fact that, unlike the relationship between the amplitude and theQ, the amount one needs to increase the cantilever drive signal does notscale directly with the change in Q.

More particularly, turning again to FIG. 5, cantilever drive circuit 109can be used in conjunction with computer 120 to compute the appropriatescale factor for the drive when changing the Q. As discussed previouslywith respect to Eqn. 1, each cantilever has a gain associated with thedevice itself (piezoelectric (η) and mechanical (γk)), and with thesensor system. Again, Eqn. 1 represents the relationship between thedesired Q, Q_(new), and the associated necessary gain, G, required toachieve the Q_(new). Because the AFM is preferably operated atresonance, we can assume the drive frequency is approximately equal tothe resonant frequency such that the relationship defined in Eqn. 5becomes,

V _(o) =γηQ _(new) V(ω)  Eqn. 7

and the gain defined in Eqn. 4 becomes, $\begin{matrix}{{G(\omega)} = {\frac{1}{\gamma\eta}\left( {\frac{1}{Q} - \frac{1}{Q_{new}}} \right)}} & \text{Eqn.~~8}\end{matrix}$

The next step in determining the appropriate drive scale factor is tosolve for Q_(new) in Eqn. 8 which becomes, $\begin{matrix}{Q_{new} = \frac{Q}{\left( {1 - {{\gamma\eta}\quad {QG}}} \right)}} & \text{Eqn.~~9}\end{matrix}$

When substituting the quantity shown in Eqn. 9 into Eqn. 7, the systemresponse becomes, $\begin{matrix}{V_{o} = {{\frac{{\gamma\eta}\quad Q}{\left( {1 - {{\gamma\eta}\quad {QG}}} \right)} \cdot {V(\omega)}} = {{\beta (G)} \cdot {V(\omega)}}}} & \text{Eqn.~~10}\end{matrix}$

As a result, when varying the gain to alter the Q, if it is desired thatV_(o) be held constant, the appropriate amount to scale the drive, V(ω),is by $\frac{1}{\left( {\beta (G)} \right)}$

or by, $\begin{matrix}{{{Drive}\quad {scale}\quad {factor}} = {\left( \frac{1 - {\gamma \quad \eta \quad {QG}}}{\gamma \quad \eta \quad Q} \right) = {\frac{1}{\left( {{\gamma\eta}\quad Q} \right)} - G}}} & \text{Eqn.~~11}\end{matrix}$

Notably, γηQ is $\frac{V_{rms}}{V_{drive}},$

i.e., the system response $\frac{V_{drive}}{V_{out}},$

and is independent of other circuitry, including the active controlcircuitry of the present invention. In addition, G is nominallypositive, such that for damping, the gain is negative. This calculationcan be implemented with analog electronics, a DSP, a microprocessor or,as shown in FIG. 5, a CPU 120. In this latter case, an output ofcomputer 120 transmits a drive scale signal indicative of the drivescale factor and applies the drive scale signal to a multiplier 122.Multiplier 122 multiplies the drive scale factor by the output ofoscillator 66 so as to scale the output.

It should be highlighted that the above equations including the drivescale factor depicted in Eqn. 11, do not need to be followed. A bruteforce approach could be followed in which the peak amplitude is foundand scaled. Performing a frequency sweep and analyzing the results canalso produce these results, even though the preferred embodiment isdescribed above. A practical “brute force” method for maintainingamplitude while changing the Q would be to first measure the RMSamplitude of the cantilever oscillation for a given drive amplitude.Thereafter, the operator can iteratively increase the damping gain, andthen the drive amplitude, to arrive at the same RMS amplitude as thepreviously measured value. These steps are then repeated until a targetdrive amplitude is reached. In this case, the target is the desiredchange in Q×A (i.e., ΔQ times the original drive amplitude).

Notably, although the embodiments shown in FIGS. 3-6 are described inconjunction with cyclical mode operation, cantilever drive circuits 62(FIG. 3) and 109 (FIG. 5) can be used in any mode (e.g., contact) tomodify damping, alter the resonance, etc.

Turning to FIG. 7, an alternate embodiment of the present inventionincludes one in which the standard AFM Z position actuator 16 (e.g., apiezo-tube actuator) of the previous embodiments is replaced with athermally responsive actuator integrated with the self-actuatedcantilever. More particularly, the alternate embodiment includes a probeassembly 140 including a self-actuated cantilever 142 having 1) a firstend 144 attached to an AFM substrate 146, 2) an elongated portion 148,and 3) a second, distal end 150 that includes a tip 152 for scanning thesurface 28 (see, e.g., FIG. 4) of a sample. Self-actuated cantilever 142also includes a Z-positioning element 154 disposed thereon.

This embodiment of the invention operates on the principal of dissimilarexpansion coefficients between cantilever 142. For instance, thecantilever 142 may be formed from a silicon material, and theZ-positioning element 154 may be formed from zinc oxide. In thepreferred embodiment of the invention, a thermal actuator, e.g., aresistive heater 156, is integrated with the cantilever by using, e.g.,a doping process.

In operation, by heating the thermal actuator (i.e., the resistiveheater 156), self-actuated cantilever 142 acts as a bimorph.Specifically, the different coefficients of thermal expansion of siliconcantilever 142 and zinc oxide Z-positioning element 154 cause cantilever142 to act as a bimorph when heated. The effect of this response is mostprominent at region 158 of cantilever 142. Notably, similar to the Zposition actuator 16 (piezo-tube Z actuator) of the previousembodiments, probe assembly 140 (and particularly the thermal actuator)can provide highly accurate imaging at relatively low scanning rates.When operating at slower imaging rates (e.g., less than 500 μm/sec), thezinc oxide element 154 is used as a reference for the thermal actuator,the thermal actuator being controlled by the feedback signal from, e.g.,control loop 54 (FIG. 4). Further, the piezoelectric effect of zincoxide Z positioning element 154 provides fast actuation of thecantilever for faster imaging rates.

Overall, by substituting the thermal actuator for the standard AFMpiezo-tube Z actuator, the vertical range of operation of theself-actuated cantilever is increased, thus providing an effectivealternative for imaging samples that have a topography that demands ahigher range of vertical operation. Hence, while the actuator of theself-actuated cantilever of the previously-described embodimentspreferably can cause movement of the cantilever over a rangeapproximately equal to 2-5 μm in the Z direction and a standard piezotube actuator operates over typically a 5-10 μm range, the thermalactuator shown in FIG. 7 can cause cantilever movement over a rangeapproximately equal to 20-100 μm. Note that, although this alternativeembodiment is described as preferably utilizing zinc oxide as thepiezoelectric element, any material having suitable piezoelectricproperties to provide Z positioning of the self-actuated cantilever 142as described herein can be used.

Next, with reference to FIG. 8, an AFM 160 particularly adapted forimaging the surfaces of biological substances is shown. AFM 160 includesa piezoelectric self-actuated cantilever 162 having a piezoelectricelement 164 disposed thereon and a tip 166 that interacts with a sample168. The sample 168 is generally immersed in a pool of fluid 170contained by a fluid cell 172. Some advantages with such a systeminclude elimination of capillary forces and the reduction of Van derWaals forces, particularly when analyzing and imaging biologicalsamples.

In this embodiment, the integrated high-speed actuator of cantilever 162replaces a conventional (e.g., piezo-stack) tip/sample actuator used bya typical biological AFM, thus enhancing the bandwidth of the mechanicalsystem, as described previously. Fluid cell 172 is formed, in part,using an AFM mount 174 having ports 176, 178 for inputting anddispensing fluid 170, respectively. Mount 174 also serves as a supportto which a fixed end of cantilever 162 is attached. A stage 179 isconfigured to accommodate sample 168 and comprises 1) a top surface 184that defines a portion of fluid cell 172 and 2) a cavity that receivesthe fluid 170 and the sample 168. O-rings 180 are disposed between anotched portion 181 of a bottom surface 182 of mount 174 and the topsurface 184 of stage 179 to seal fluid cell 172 from the surroundingenvironment. Also, the piezoelectric (e.g., ZnO) element 164 ismicromachined and therefore very small and very fast. For example, theresonance of a ZnO cantilever is approximately one hundred times greaterthan the resonance of a bulk piezo-tube actuator. For a givenoperational condition in the so-called contact mode, any increase inactuator resonant frequency will increase data acquisition/imaging speedin the same proportion.

As noted above, the Q of the cantilever resonance is damped by theviscous environment in which this embodiment of the invention operates,thus lessening the bandwidth limitations caused by a large Q (discussedabove). Nevertheless, these speed advantages are countered by theincreased drive oscillation required to operate the damped cantilever.

In operation, the resonant nature of the cantilever 162 stores theexcitation energy and amplifies the movement of the tip 166. The qualityfactor (Q) is representative of this resonant amplification and isdependent on the damping in the resonant system. In fluid, where viscousforces are much greater than in air, the Q can drop significantly. Withthis limitation on resonant amplification, the system must excite thecantilever 162 almost the same amount as the desired tip amplitude inorder to drive the cantilever at its resonance. For known systems whichexcite the cantilever resonance with a piezotube or piezo-stack actuatorlocated beneath the cantilever die, the entire piezo-stack andcantilever die are moving distances commensurate with the tip movement.Driving the cantilever in this fashion excites resonances in fluid cell172, e.g. due to acoustic excitation, thus disrupting imagingcapabilities. The present invention substantially subverts this problemby using the piezoelectric element 164 of cantilever 162 to excite thecantilever beam. This construction integrates the entire oscillatingexcitation onto the AFM cantilever 162 and, therefore, virtuallyeliminates the acoustic excitation of the fluid cell 172.

During operation in fluid, in contrast to the previously describedembodiments, the electrodes (not shown) coupled to the substrate ofself-actuated cantilever 162 will potentially interface with fluid 170.This fluid/electrode interaction exposes the electrical system of AFM160 to a high risk of short. Therefore, the electrodes should bepassivated, e.g., insulated from fluid 170. Preferably, an insulatinglayer 167 is deposited generally over the entire cantilever structure,usually as a final step in the fabrication of cantilever 162. Dependingupon the process employed, the insulating layer 167 can be removed fromthe apex of tip 166. Preferably because the design and composition ofthe tip 166 affects imaging resolution, whatever the passivationprocess, care should be taken to ensure that the insulating layer 167does not cover the apex of the tip 166 to optimize imaging resolution.

Insulators usable as layer 167 include silicon nitride, silicon dioxide,and polymers including PMMA, photoresist, RTV of any viscosity andpolyimide. During cantilever fabrication, nitride and oxide may bedeposited on cantilever 162, preferably by either chemical vapordeposition (CVD), low pressure CVD or plasma enhanced CVD.Alternatively, sputtering or evaporation techniques may be used todeposit such insulators. On the other hand, polymers preferably aredeposited by spin coating or vapor phase deposition.

Another equally viable passivation technique is “shadow masking” theapex of tip 166 and spraying-on one of various polymers including PMMA,dissolved TEFLON®, photoresist, or PDMS (polydimethylsiloxaneelastomer). The sprayer used in such a process can be, for example, acommercial air-brush, and the shadow mask can be a micropipette or apulled pipette. Alternatively, cantilever 162 can be passivated bydipping the entire probe, except for the tip 166, into PMMA,photoresist, TEFLON® or PDMS, and then allowing the device to cure.Notably, the two methods described immediately above are best performedonce the cantilever 162 is mounted onto a robust substrate. Further, thewire bonds (not shown) which connect the cantilever die to thesubstrate, and all other contacts to outside leads are preferably coatedwith an insulator such as Dow Corning 3140RTV.

The process for depositing the insulating layer 167 must be compatiblewith the specialized process for forming the integrated piezoelectricactuator of cantilever 162. In particular, the insulating layer shouldbe deposited on the cantilever 162 with a controlled stress because thefilm typically creates a bimorph with the cantilever which can causeunwanted curvature in the device. In fact, if this stress is notcontrolled, the stress could potentially “rip” the cantilever 162 fromits base. There are a variety of conventional methods to control thestress when passivating the cantilever with either a deposited film or apolymer film. For deposited films, temperature, gas ratios, pressures,power (when utilizing plasma deposition), etc. are appropriately variedto control the final film stress. The final parameters depend on thespecifications of the film and the equipment being used. Similarly,polymer film stress can be controlled by varying applicationtemperature, rate of cure, polymer structure, etc. These parameters arealtered in conventional fashion.

According to another preferred embodiment, the AFMs described herein canbe operated in a gaseous environment. In particular, corrosive, reactiveor otherwise contaminating gases can be introduced to the AFM platformso as to perform, for example, real-time observation of chemicalreactions between the gas and the sample. Similar to operation in fluid,the AFM cantilever is passivated as described above to maintain reliablecantilever operation. Without passivating the cantilever, the corrosivegasses can damage the cantilever or, at least, have a detrimental affecton cantilever operation. One method of introducing a gas includesenclosing the entire AFM in a sealed chamber 41 (FIGS. 4 and 6) andintroducing the gas within the chamber. Alternatively, as shown in FIG.9, gasses can be supplied to an AFM 190 having a probe assembly 192including a tip 194 via unconstrained blowing of a compressed gas 199from a nozzle 198 towards sample 196. Yet another alternative is to usea fluid cell, such as that shown in FIG. 8 and described above, except agas is introduced at inlet 176 rather than a liquid. According to thislatter alternative, the chemical reaction is isolated within the fluidcell, which may be required for some applications.

Although the preferred embodiments have been generally described asapparatus and methods for imaging the surface of a sample, thetechniques described herein can be implemented for single pixelmeasurements. Rather than imaging, i.e., acquiring and conditioning datafrom a scan line or a scan area containing many pixels, the AFM isoperated to obtain data pertaining to a single pixel or point associatedwith the sample. In particular, the tip is oscillated perpendicularly tothe sample, as various measurements are made throughout each oscillationcycle. More particularly, turning to FIG. 10, a method 200 of collectingdata for a single pixel measurement includes, after initialization andstart-up at Step 202, beginning a data acquisition cycle to cause thetip to move toward the sample at Step 204. As the tip approaches thesample, tip-sample interaction is monitored. In particular, at Step 206,the attraction forces between the tip and sample are measured and storedfor further analysis. Then, during a second part of the cycle, the tipcontacts the sample surface and, at Step 208, the degree to which thesample “deforms” is measured. At Step 210 , the system determines thecompliance of the sample under test and stores the data. Finally, atStep 212, a third part of the cycle causes the tip to pull away from thesample, and adhesion forces are measured and bond strength isdetermined. The method 200 then returns operation of the system back toStep 204 to collect data for additional cycles relating to the same oranother pixel. Overall, the measurements made during one (or more)cycles can be collected and processed to create a profile of theproperties of the sample.

Although the best mode contemplated by the inventors of carrying out thepresent invention is disclosed above, practice of the present inventionis not limited thereto. It will be manifest that various additions,modifications and rearrangements of the features of the presentinvention may be made without deviating from the spirit and scope of theunderlying inventive concept.

What is claimed is:
 1. A method of actively changing the bandwidth ofamplitude detection of an AFM operating in cyclical mode comprising:providing a self-actuated cantilever having a piezoelectric elementdisposed thereon; providing a damping feedback circuit; applying anoscillating voltage signal to the piezoelectric element to oscillate theself-actuated cantilever at a resonant frequency; scanning a surface ofa sample with the self-actuated cantilever; generating a deflectionsignal in response to a deflection of the self-actuated cantileverduring said scanning step; and using the damping feedback circuit toactively modify the quality factor (Q) associated with the self-actuatedcantilever in response to the deflection signal.
 2. The method of claim1, wherein the damping feedback circuit includes a phase shifter, andsaid using step is performed by (1) phase shifting the deflection signalwith the phase shifter and (2) adding the phase shifted deflectionsignal to the oscillating voltage signal.
 3. The method of claim 1,wherein the damping feedback circuit includes a differentiator, and saidusing step is performed by (1) differentiating the deflection signalwith the differentiator, (2) applying a gain to the differentiateddeflection signal to generate a damping signal and (3) combining thedamping signal with the oscillating voltage signal.
 4. The method ofclaim 3, wherein the gain is dependent upon a selected Q, (Q_(new)),which causes the AFM to operate according to a desired operating state.5. The method of claim 4, wherein the gain is characterized by thefollowing equation,${G(\omega)} = {\quad \frac{\omega}{\omega_{0}}\frac{1}{\gamma \quad \eta}\left( {\frac{1}{Q} - \frac{1}{Q_{new}}} \right)}$

wherein ω is an operating frequency of the cantilever, ω₀ is theresonant frequency of the cantilever, Q is the native Q, and γ and η areconstants associated with the cantilever.
 6. The method of claim 5,wherein G(ω) is determined using a microprocessor.
 7. The method ofclaim 1, further comprising the step of scaling the oscillating voltageso as to hold the amplitude of the resonance of the cantilever generallyconstant during said using step.
 8. The method of claim 7, wherein saidscaling step includes multiplying said oscillating voltage signal by adrive scale factor.
 9. The method of claim 8, wherein said drive scalefactor is ${\frac{1}{{\gamma\eta}\quad Q} - G},$

and wherein Q is the native Q, G is a gain applied to modify Q to aQ_(new), and γ and η are constants associated with the cantilever. 10.The method of claim 1, wherein the AFM is configured for operation in afluid by placing a sample in a fluid cell.
 11. The method of claim 10,wherein the fluid cell has an inlet and an outlet and the fluid flowsfrom the inlet to the outlet during operation.
 12. The method of claim10, wherein the cantilever is passivated for operation in the fluid byinsulating electrodes of the piezoelectric element from the fluid. 13.The method of claim 12, wherein the electrodes are insulated with apolymer.
 14. The method of claim 13, wherein the polymer is PDMS. 15.The method of claim 1, wherein the damping feedback circuit includes aproportional gain stage, and further comprising the step of operatingthe proportional gain stage so as to change the resonant frequency. 16.An AFM for analyzing a surface of a sample in cyclical mode, the AFMcomprising: a self-actuated cantilever having a piezoelectric elementdisposed thereon; an oscillator that applies an oscillating voltagesignal to the piezoelectric element to oscillate the self-actuatedcantilever; a deflection detector that generates a deflection signal inresponse to a deflection of said self-actuated cantilever; and a dampingfeedback circuit that actively modifies the quality factor (Q)associated with the self-actuated cantilever in response to thedeflection signal to actively modify the bandwidth of amplitudedetection of the AFM.
 17. A method of analyzing a sample in cyclicalmode with a probe-based AFM having a self-actuated cantilever and aZ-position actuator, the self-actuated cantilever having a Z-positioningelement integrated therewith, the method comprising: applying anoscillating driving voltage to the Z-positioning element to oscillatethe self-actuated cantilever and to cause a tip of the cantilever tointermittently contact a surface of the sample; generating a deflectionsignal in response to a deflection of the self-actuated cantileverduring said applying step; generating a cantilever control signal inresponse to said deflection signal; maintaining a parameter associatedwith the oscillation of the self-actuated cantilever at a constant valueby servoing the position of the self-actuated cantilever relative to thesample in response to said cantilever control signal; generating aposition control signal in response to said cantilever control signal;controlling the Z-position actuator in response to said position controlsignal; and using a damping feedback circuit to generate a dampingfeedback signal in response to said deflection signal and modifying thequality factor (Q) associated with the self-actuated cantilever withsaid damping feedback signal.
 18. The analyzing method of claim 17,further comprising the step of imaging the surface by scanning a surfaceof the sample with the self-actuated cantilever.
 19. The analyzingmethod of claim 17, wherein said damping feedback signal is generated byphase shifting said deflection signal.
 20. The analyzing method of claim19, wherein said deflection signal is phase shifted by about 90 degrees.21. The analyzing method of claim 17, wherein said modifying stepcomprises adding said damping feedback signal to said oscillatingdriving voltage.
 22. The analyzing method of claim 17, wherein saiddamping feedback circuit includes a differentiator which differentiatessaid deflection signal.
 23. The analyzing method of claim 22, furtherincluding a gain stage that applies a gain to said differentiateddeflection signal to produce said damping feedback signal.
 24. Theanalyzing method of claim 23, wherein the gain is dependent upon adesired Q (Q_(new)), which causes the AFM to operate according to adesired operating state.
 25. The analyzing method of claim 24, whereinthe desired operating state is an increased data collection speed. 26.The analyzing method of claim 23, wherein the gain is computed accordingto the following equation,${G(\omega)} = {\quad \frac{\omega}{\omega_{0}}\frac{1}{\gamma \quad \eta}\left( {\frac{1}{Q} - \frac{1}{Q_{new}}} \right)}$

wherein ω is an operating frequency of the cantilever, ω₀ is a resonantfrequency of the cantilever, Q is the native Q, Q_(new) is a desired Qand γ and η are constants associated with the cantilever.
 27. Theanalyzing method of claim 17, wherein said applying step causes the tipto contact a point on the surface over a cycle so as to make at leastone single pixel measurement.
 28. The analyzing method of claim 27,further comprising the step of measuring an attraction force between thetip and the surface during a first part of the cycle.
 29. The analyzingmethod of claim 28, further comprising the step of measuring adeformation of the surface during a second part of the cycle.
 30. Theanalyzing method of claim 29, further comprising the step of determininga compliance of the sample based on the measured deformation.
 31. Theanalyzing method of claim 27, further comprising the step of measuringan adhesive force during a third part of the cycle.
 32. A method ofanalyzing a sample in cyclical mode with a probe-based AFM, the methodcomprising: providing a self-actuated cantilever and a piezo-tubeZ-position actuator, said self-actuated cantilever including aZ-positioning element integrated therewith; oscillating, with saidZ-positioning element, said self-actuated cantilever at a cantileverresonant frequency and at a predetermined amplitude of oscillation so asto cause a tip of the cantilever to intermittently contact a surface ofthe sample; effectuating relative scanning motion between saidself-actuated cantilever and the sample; generating a deflection signaleffectuating step; generating, with a first feedback loop, a cantilevercontrol signal in response to said deflection signal; maintaining saidamplitude of oscillation at a constant value in response to saidcantilever control signal; using said cantilever control signal as anerror signal in a second feedback loop to control the Z-positionactuator, wherein said first feedback loop is nested within said secondfeedback loop; and damping said self-actuated cantilever with acantilever drive circuit to actively modify the quality factor (Q) ofthe cantilever resonant frequency during said effectuating step.
 33. Themethod of claim 32, wherein said applying step causes the tip tointermittently contact a point on the surface so as to make a singlepixel measurement.
 34. The method of claim 32, further comprisingimaging the surface by scanning a surface of the sample with theself-actuated cantilever.
 35. The analyzing method of claim 32, whereinsaid damping step is performed by (1) phase shifting said deflectionsignal to produce a phase shifted deflection signal and (2) adding saidphase shifted deflection signal to said oscillating voltage.
 36. Theanalyzing method of claim 35, wherein said deflection signal is phaseshifted by about 90 degrees.
 37. The analyzing method of claim 32,wherein said damping step includes generating a damping feedback signalby differentiating said deflection signal and applying a gain to thedifferentiated signal.
 38. The analyzing method of claim 37, wherein thegain is equal to,${G(\omega)} = {\quad \frac{\omega}{\omega_{0}}\frac{1}{\gamma \quad \eta}\left( {\frac{1}{Q} - \frac{1}{Q_{new}}} \right)}$

wherein ω is an operating frequency of the cantilever, ω₀ is thecantilever resonant frequency of the cantilever, Q is the native Q, andγ and η are constants associated with the cantilever and Q_(new) isselected to achieve a desired operating state.
 39. The analyzing methodof claim 38, wherein the operating state is increased imaging speed. 40.The analyzing method of claim 38, wherein the cantilever drive circuitincludes a proportional gain stage, and further comprising the step ofoperating the proportional gain stage so as to change the cantileverresonant frequency.
 41. A cyclical mode AFM for scanning a surface of asample at a predetermined scanning rate, the AFM comprising: aself-actuated cantilever comprised of an elongated member and having aZ-positioning element integrated therewith; a Z-position actuator thatdisplaces the sample; an oscillator that applies an oscillating voltageto said cantilever to oscillate said cantilever at a cantilever resonantfrequency, said oscillating voltage having a predetermined amplitude; afirst feedback loop that generates a first feedback signal in responseto cantilever deflection during scanning, wherein said first feedbacksignal maintains said amplitude of oscillation at a constant value; asecond feedback loop which is responsive to said first feedback signalto generate a second feedback signal that controls Z-position actuator;and wherein said first feedback loop includes a damping circuit thatactively modifies the quality factor (Q) of the cantilever resonance toincrease the scanning rate.
 42. The cyclical mode AFM of claim 41,wherein said Z-position actuator includes a heating element disposed onsaid self-actuated cantilever, said heating element being response tosaid second feedback signal to heat said self-actuated cantilever. 43.The cyclical mode AFM of claim 42, wherein said Z-positioning elementcomprises zinc oxide and said elongated member comprises silicon, andwherein said self-actuated cantilever is configured to act as a bimorphwhen said heating element heats said self-actuated cantilever inresponse to said second feedback signal.
 44. A method of activelychanging the bandwidth of amplitude detection of an AFM, the methodcomprising: providing a self-actuated cantilever having a piezoelectricelement disposed thereon; providing a cantilever drive circuit; drivingthe self-actuated cantilever at a cantilever resonant frequency with anoscillating voltage signal; scanning a surface of a sample with theself-actuated cantilever; during said scanning step, generating adeflection signal in response to a deflection of the self-actuatedcantilever; in response to the deflection signal, operating thecantilever drive circuit to actively modify a quality factor (Q)associated with the self-actuated cantilever.
 45. The method of claim44, wherein the cantilever drive circuit includes a phase shifter, andsaid operating step comprises (1) phase shifting the deflection signalwith the phase shifter and (2) adding the phase shifted deflectionsignal to the oscillating voltage signal.
 46. The method of claim 44,wherein the cantilever drive circuit includes a differentiator, and saidoperating step comprises (1) differentiating the deflection signal withthe differentiator, (2) applying a gain to the differentiated deflectionsignal to generate a damping signal, and (3) combining the dampingsignal to the oscillating voltage signal.
 47. The analyzing method ofclaim 44, wherein the cantilever drive circuit includes a proportionalgain stage, and further comprising the step of operating theproportional gain stage so as to change the cantilever resonantfrequency.
 48. An AFM for analyzing a surface of a sample, the AFMcomprising: a self-actuated cantilever having a piezoelectric elementdisposed thereon; a source which is configured to drive theself-actuated cantilever at a cantilever resonance; a deflectiondetector that is configured to generate a deflection signal in responseto a deflection of said self-actuated cantilever; and a cantilever drivecircuit that is configured to actively modify a quality factor (Q)associated with the self-actuated cantilever in response to thedeflection signal to actively modify a bandwidth of amplitude detectionof the AFM.
 49. The method of claim 48, wherein said cantilever drivecircuit includes a proportional gain stage to selectively change thecantilever resonant frequency.